Abstract
Based on the recent formulation of a general scheme to construct boundary Lax pairs, we develop this systematic construction for the A n ( 1 ) affine Toda field theories (ATFT). We work out explicitly the first two models of the hierarchy, i.e. the sine-Gordon ( A 1 ( 1 ) ) and the A 2 ( 1 ) models. The A 2 ( 1 ) Toda theory is the first non-trivial example of the hierarchy that exhibits two distinct types of boundary conditions. We provide here novel expressions of boundary Lax pairs associated to both types of boundary conditions.
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